Revision d61a6815-b41b-491c-b449-7f652e06c04b - Code Golf Stack Exchange

# JavaScript (ES6), 83 bytes

Expects `(u)(v)`.

<sup>_Disclaimer: Either that's correct, or I completely misunderstood the challenge._</sup>

<!-- language-all: lang-javascript -->

 u=>v=>[0,1,2,4].reduce((p,i)=>p.map(n=>i&&n+u[i%=7]*v[j%=7]-u[j++]*v[i++],j=i*3),u)

[Try it online!](https://tio.run/##lVJNj9MwEL33V8xaYjVu0tCkwEqsEsSBAweuuWQr5OaDutu1Kzdxt4Ldv8EP4oeVcbxVvxCIS8aeefPevHEWwop1aeSqHSld1bsm3XVpZtOsGIdxmIRvppGpq66sEVeh5Gm2ih7EClWayetrFXSFfJXeTIe2WLg46opFELirpBAuUjmc8LDju1KrdQs5pFBEUfTRGLHFGx7d19s18untwNeNUFVel602BPwKaQZ5r9Yfv4h2HjmEfkAOQ4jH8APG/HYwyKNGm0@inOPWAb8PAByfXtbRUn9Dz/G4L/liCx1p@NK9KwUupPDIifEAsn8EbU9BGwI12HG0L2nZ4OZobVBy17yCAK6uypCGhgxiDu3c6A0wqaxYygpMve6WLTtmVsS8iRqpqs@qqh/ROp69iqnbzih4VvABcFOoqRttFNONjRi8BxYwTpKsZvRFRR/SpDTAuBd54tFCS4UMmPPz5FbpZQXJ9utullobPN988vYdh9cu7B9u9r8NeUwdh@dGHkKenKU8dv@K7E4JG//6ObPJnXKOGszj/mX6pQiSsZxjnhxyM587cXlOOUNHahN@IHUk/JTZM50QvRixl0Zscpma/MsbjRHQFDTKZD@J9fbQhiD7H8hS2iaFnJJPO/mrL@9qwgO0SX84kPreS2aqJX3NCRxz734D "JavaScript (Node.js) – Try It Online")

### Commented

 u => // u[] = first vector
 v => // v[] = second vector
 [0, 1, 2, 4] // lookup list
 .reduce((p, i) => // for each value i with p[] as the accumulator:
 p.map(n => // for each value n in p[]:
 i && // force to zero if i = 0
 n + // otherwise, take the current value n
 u[i %= 7] * // and add u[i] * v[j] - u[j] * v[i]
 v[j %= 7] - // where both i and j are reduced modulo 7
 u[j++] * // and incremented afterwards
 v[i++], //
 j = i * 3 // start with j = i * 3
 ), // end of map()
 u // start with p[] = u[] (but the content of p[]
 // is cleared on the first iteration)
 ) // end of reduce()